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Keywords:

  • time-dependent density functional theory;
  • nonadiabatic couplings;
  • quantization;
  • polyatomic;
  • Jahn–Teller;
  • Renner–Teller

Abstract

We present extensive calculations on the quantization behaviors of first-order nonadiabatic couplings (NAC) in polyatomic systems, using the method based on time-dependent density functional theory (TDDFT). Along circular contours around Jahn–Teller conical intersections at various symmetries, such as D4h and D6h, the angular NAC are found to show apparent dependence on the contour angle, no matter how close the conical intersections are approached. This is in contrast to that the angular NAC in triatomic Jahn–Teller systems (D3h) converge to the quantized value of 1/2. The oscillatory feature of our calculated curves qualitatively resembles the analytic result of angular NAC around elliptic conical intersections in the small-displacement limit. Furthermore, by performing the integral along the whole contour, the quantization rule on the integral of the angular NAC holds for all cases, which gives the geometric phase with a value of π. On the other hand, the angular NAC in the immediate vicinity of Renner–Teller intersections are shown to be always 1. This observation can be understood from the fact that the molecular symmetry property of the Renner–Teller intersections is always determined by the linear atomic chain. Further analysis of our results on Renner–Teller systems shows that although the quantization behavior of angular NAC can determine all NAC vectors on each atom for the triatomic systems, it cannot for the systems with more than three atoms. The NAC vectors of the latter systems are found to show both common and distinct features with respect to the atomic number and species by our TDDFT calculations. © 2012 Wiley Periodicals, Inc.